Question

I am trying to figure out the complexity of the function below. I am guessing it would be O(n), because the Random class produces a random number in O(1) and put() and containsKey() are also O(1).

But since there is a do-while inside the loop, I wasn’t sure if the complexity would change since random() could be called multiple times if the value is contained in the HashMap. I would appreciate any help!

HashMap<Integer, Integer> values = new HashMap();
for(int i=0 ; i<a.length; i++){
    do{
        // set variable random to some integer between 0 and a.length using Random class in Java, 0 is included. 
    }while(values.containsKey(random) == true);
    b[i] = a[random]
    values.put(random,0);
}

The length of the array is around 1000 and the random number generated is anywhere from 0 to 999.

Answer 1

 Building the map elements: O(n)--->for loop

 Checking if the random value is in the map: O(1+α) with a good hash function
 Trying to find a random value which your map does not have: O(n)
 (because you are using integer. Even floats would give very good resolution)


 array length=1000, random-value range=1000(from 0 to 999)
 think you are at the last element. probability of getting proper value is:
 %0.1 which takes an average of 1000 trials only for the last element (n)
 nearly same for the (n-1)st element (%0.2-->n/2 trials)
 still nearly same for (n-2)nd element (%0.3-->n/3 trials)

 what is n+n/2 + n/3 + n/4 + n/5  ... + 1 = a linear function(O(n)) +1 
 α2=1 but neglecting :) and this is on top of a O(n)


 Result: O(n*n+α*n*n) close to O(n*n)